My son is 9 months old and he had a mild fever for three days.
We gave him Baby Tylenol and the fever went away.
However, after the fever, he now has a rash. A doctor friend of our
family said that it is probably a viral infection.
The rash is now all over is body (from head to toe).

I would like to know, how long does the rash usually last and what should I
do to sooth his itchiness? Is there a cream I can apply?

I would suggest a calendula salve. Calendula is completely natural and it is known for healing the skin. The commercial products you buy are filled with chemicals. The Tylenol doesn't fix the fever, it just suppresses the symptoms which would be a fever. A fever is an indicator that the body is fighting off the infection and when you give Tylenol, it interferes with that. A fever is normal and a healthy part of the body's defense system. Try the wet socks method, if you are not sure what this is, you can look it up. I hope your baby feels better soon.

Sounds like Roseola. Typically you get a high fever for about 3-5 days, then when it breaks, you have a pink "lacey" rash all over the body, but mostly on the trunk. I hope your babe feels better soon. Dd had it this year, and she was miserable. They also usually have a huge boost of immunity after, which is great. Roseola isn't dangerous.
ETA: the rash usually isn't itchy, and disappears after 2 days.